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Title:

Infill Asymptotics Inside Increasing Domains for the Least Squares Estimator in Linear Models

Description:

α-mixing, asymptotic normality, consistency, errors-in-variables, infill asymptotics, least squares estimator, linear model, spatial observations

α-mixing, asymptotic normality, consistency, errors-in-variables, infill asymptotics, least squares estimator, linear model, spatial observations Minimize

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article

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Title:

Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=B

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A multivariate measurement error model AX≈B is considered. The errors in [A,B] are rowwise independent, but within each row the errors may be correlated. Some of the columns are observed without errors, and in addition the error covariance matrices may differ from row to row. The total covariance structure of the errors is supposed to be known u...

A multivariate measurement error model AX≈B is considered. The errors in [A,B] are rowwise independent, but within each row the errors may be correlated. Some of the columns are observed without errors, and in addition the error covariance matrices may differ from row to row. The total covariance structure of the errors is supposed to be known up to a scalar factor. The fully weighted total least squares estimator of X is studied, which in the case of normal errors coincides with the maximum likelihood estimator. We give mild conditions for weak and strong consistency of the estimator, when the number of rows in A increases. The results generalize the conditions of Gallo given for a univariate homoscedastic model (where B is a vector), and extend the conditions of Gleser given for the multivariate homoscedastic model. We derive the objective function for the estimator and propose an iteratively reweighted numerical procedure. Copyright Springer-Verlag 2004 ; Linear errors-in-variables model, Elementwise-weighted total least squares, Consistency, Iteratively reweighted procedure, 65F20, 62J05, 62F12, 62H12 Minimize

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article

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Title:

Non-Existence of the First Moment of the Adjusted Least Squares Estimator in Multivariate Errors-in-Variables Model

Description:

Adjusted least squares, Equation error model, Functional model, Infinite first moment, Linear multivariate error-in-variables model, Structural model, 62J05, 62H12, 62H10

Adjusted least squares, Equation error model, Functional model, Infinite first moment, Linear multivariate error-in-variables model, Structural model, 62J05, 62H12, 62H10 Minimize

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article

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Quasi Score is more Efficient than Corrected Score in a Polynomial Measurement Error Model

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Quasi score, Corrected score, Polynomial model, Measurement errors, Efficiency, Structural methods, Functional methods

Quasi score, Corrected score, Polynomial model, Measurement errors, Efficiency, Structural methods, Functional methods Minimize

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article

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Three estimators for the poisson regression model with measurement errors

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Poisson regression model, measurement errors, corrected score estimator, structural quasi score estimator, naive estimator

Poisson regression model, measurement errors, corrected score estimator, structural quasi score estimator, naive estimator Minimize

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Title:

Statistical Inference with Fractional Brownian Motion

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fractional Brownian motions, hypothesis testing, goodness-of-fit test, volatility estimation

fractional Brownian motions, hypothesis testing, goodness-of-fit test, volatility estimation Minimize

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article

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Title:

STATIC LOWER BOUNDS FOR GAUSSIAN RISKS AND COMONOTONIC ASSET PRICES ON ARBITRAGE-FREE MARKET

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Consider a Gaussian random vector X=(X1,…Xn) of which we can only observe the marginal distributions. Our goal is to construct an optimal static lower bound for gB(X,K)=(S-K)+ where S=X1+…+Xn, in terms of random variables (rv’s) gC(Xi,Ki)=(Xi-Ki)+ and gP(Xi,Ki)=(Ki-Xi)+, respectively. We interpret Xi’s as financial or actuarial risks. We mention...

Consider a Gaussian random vector X=(X1,…Xn) of which we can only observe the marginal distributions. Our goal is to construct an optimal static lower bound for gB(X,K)=(S-K)+ where S=X1+…+Xn, in terms of random variables (rv’s) gC(Xi,Ki)=(Xi-Ki)+ and gP(Xi,Ki)=(Ki-Xi)+, respectively. We interpret Xi’s as financial or actuarial risks. We mention the paper of Hobson et al. (2005) who studied a lower bound for basket options of two components, which is a special case of our problem for nonnegative rv’s Xi’s and n=2. A related problem of upper bound for basket options is investigated, e.g., in Rüschendorf (2005), p.34, where comonotonic joint distributions of asset prices are involved. Below we present the main our result. Let μi and σi 2 be the fixed values of mean and variance of Xi, i=1,…,n, σm 2 be the largest of those variances, σ=( σm-∑i≠mσi)+ and M=μ1+…+μn. If σ>0 then for all nonrandom vectors x, it holds: gB(x,K)≥gC(xm,Km)- ∑i≠mgP(xi,Ki)=:gSR + (x) , moreover min EgB(X,K)=EgB(X *,K)=EgSR + (X * ). Hereafter minimum is taken over all possible Gaussian vectors X with fixed marginal distributions, and X * =(- σ1γ,-σ2γ,…,+σmγ,-σm+1γ,…,-σnγ) with γ~N(0,1), and Km=σmσ-1 (K-M)+ μm, Ki =- σiσ-1 (K-M)+ μi, i≠m. If σ=0 and M≤K then gB(x,K)≥0 and min EgB(X,K)=0. Thus, in this case an optimal lower bound is equal to zero. Finally, if σ=0 and M>K then for any Δ and all nonrandom x, it holds: gB(x,K) ≥ gC(xm,K+Δ)- ∑i≠mgP(xi,-Δ(n-1)-1)=: gSR 0 (x,Δ) , moreover min EgB(X,K)=M-K=limΔ→+∞EgSR 0 (X,Δ). Therefore, in this case the rv’s gSR 0 (x,Δ) with Δ>0 provide the asymptotically optimal lower bounds. Also, for an arbitrage-free market with one underlying asset, we show that subsequent values of the asset price form a comonotonic random vector only under a deterministic linear relationship (see [1] for the definition of comonotonic vector). Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-03-16

Source:

http://www.stat.uni-muenchen.de/%7Emahling/Kolloquium/ss09/090515_Kukush.pdf

http://www.stat.uni-muenchen.de/%7Emahling/Kolloquium/ss09/090515_Kukush.pdf Minimize

Document Type:

text

Language:

en

Subjects:

options ; Insurance ; Mathematics and Economics ; v.37 ; p.553-572 ; 2005

options ; Insurance ; Mathematics and Economics ; v.37 ; p.553-572 ; 2005 Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Comonotonic modification of random vector in its own probability space

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-10-25

Source:

http://www.econ.kuleuven.ac.be/tew/academic/actuawet/pdfs/ComonotProbSpace-110110.pdf

http://www.econ.kuleuven.ac.be/tew/academic/actuawet/pdfs/ComonotProbSpace-110110.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Comonotonic random vector ; comonotonic modi…cation ; non-atomic probability

Comonotonic random vector ; comonotonic modi…cation ; non-atomic probability Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

On the Computation of the Multivariate Structured Total Least Squares Estimator

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A multivariate structured total least squares problem is considered, in which the extended data matrix is partitioned into blocks and each of the blocks is Toeplitz/Hankel structured, unstructured, or noise free. Two types of numerical solution methods for this problem are proposed: i) standard local optimization methods in combination with effi...

A multivariate structured total least squares problem is considered, in which the extended data matrix is partitioned into blocks and each of the blocks is Toeplitz/Hankel structured, unstructured, or noise free. Two types of numerical solution methods for this problem are proposed: i) standard local optimization methods in combination with efficient evaluation of the cost function and its first derivative, and ii) an iterative procedure proposed originally for the element-wise weighted total least squares problem. The computational efficiency of the proposed methods is compared with this of alternative methods. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-08-31

Source:

ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/markovsky/reports/02-203.ps.gz

ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/markovsky/reports/02-203.ps.gz Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Remarks on quantiles and distortion risk measures

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Distorted expectations can be expressed as weighted averages of quantiles. In this note, we show that this statement is true, but that one has to be careful with the correct formulation of it. Furthermore, the proofs of the additivity property for distorted expectations of a comonotonic sum that appear in the literature often do not cover the ca...

Distorted expectations can be expressed as weighted averages of quantiles. In this note, we show that this statement is true, but that one has to be careful with the correct formulation of it. Furthermore, the proofs of the additivity property for distorted expectations of a comonotonic sum that appear in the literature often do not cover the case of a general distortion function. We present a straightforward proof for the general case, making use of the appropriate expressions for distorted expectations in terms of quantiles. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-22

Source:

http://www.econ.kuleuven.ac.be/tew/academic/actuawet/pdfs/2012-10-17-QuantilesDistExp.pdf

http://www.econ.kuleuven.ac.be/tew/academic/actuawet/pdfs/2012-10-17-QuantilesDistExp.pdf Minimize

Document Type:

text

Language:

en

Subjects:

comonotonicity ; distorted expectation ; distortion risk measure ; TVaR

comonotonicity ; distorted expectation ; distortion risk measure ; TVaR Minimize

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